Around Two thousand five hundred years ago, a Greek mathematician, Pythagoras, invented the Pythagorean Theorem. The Theorem was related to the length of each side of a right-angled triangle. In a right-angled triangle, the square on the hypotenuse, the side opposite to the right angle, equals to the sum of the squares on the other two sides. (148, Poskitt) To know more about this famous theorem, we can look at the other forms of the Pythagorean Theorem, such as it can also be written as c^2-a^2=b^2 which is for reverse operations like finding side b with the data of a and c. Meanwhile, the proofs of the theorem can make us understand more about the invention of the theorem and how Pythagoras figured it out. And with the invention of this theorem, we shall look into where this theorem was used in these days and how important it is.
Pythagoras was a Greek mathematician born nearly two thousand and sixty years ago. He loved maths when he was very young and spent his whole time investigating maths. He found that “In a right-angled triangle, the square on the hypotenuse, the side opposite to the right angle, equals to the sum of the squares on the other two sides.” (148, Poskitt)
He proved that all right-angled triangles worked with this theorem
c a a^2+b^2=c^2
b
To calculate the length of the hypotenuse, we can simply square each of the perpendicular sides a and b and add them together. Afterwards, we have to root the answer (√c), which is the reverse of square. That means, the theorem can also be written as√(〖(a〗^2+b^2 ))=c. This equation means you first add the square of a" and " b, root it, then it would equal c, which is exactly the same as the original form of the theorem.
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...d triangle. It is an equation a^2+b^2=c^2 but also can be turned into different forms like √(〖(a〗^2+b^2 ))=c or even take a^2 and write as b^2=c^2-a^2. With the algebraic equations the length of each side of an right-angled triangle can easily be calculated. Meanwhile, there are a lot of ways to proof the Pythagorean Theorem, they were all invented by different mathematicians aroung the world at different time, and can proof the theorem using squares, rectangles, trapezium, circles and much more shapes. There are over three hundred proofs currently. With all these different proofs we can believe that the theorem is most likely correct. Moreover, the Pythagorean Theorem can help architects and contruction workers, or even geologists in different ways to help their calculations be easier. The Pythagorean Theorem is very important on the whole in the mathematics world.
Through history, as said before, many philosophers have supported and developed what Pythagoras first exposed to the world. One of the most important philosophers to support Pythagoras’s ideas was Plato. In some of his writings he discusses the creation of the universe based on the musical proportions discovered by Pythagoras (Timaeus), and the explanation of the sound emitted by the planets, which is exposed in the “Myth of Er” in The Republic. It talks about a man who died and came back to life who narrates how he saw the space and how, in every “sphere,” there was a being singing constantly, each one in a different tone, so a perfect harmony was built. Nevertheless, not everyone agreed with this theory, being one of its most important critics Aristotle, who claimed that Plato’s arguments where false in his text On the Heavens. He acknowledges that it is a creative and innovative theory, but it is absurd to think that such music, which is imperceptible to us, exists in a harmonic way up in the heavens. I am not going to go deeper into that for it is not relevant for the text. As the years went on, many people continued developing this theory. Nevertheless, this philosophical theory, not truly explained until later on, was an inspiration for many artists and that is why not only philosophers but many other artists mention and base their works upon this theory.
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
Here Pythagoras, better known as a mathematician for the famous theorem named for him, applied theoretical mathematics and the theory of numbers to the natural sciences (Nordqvist, 1). Pythagoras equated the duration of the lunar cycle to the female menstrual cycle and related the biblical equation of infinity as the product of the number seventy and forty to the normal length of pregnancy at 280 days (Nordqvist, 1). More practical, Pythagoras also contributed the idea of medical quarantine to the practice of medicine setting a forty-day period standard quarantine to avoid the spread of disease. While Pythagoras chose the number forty for its perceived divine nature his practical application of a quarantine must have been based on the observation that in some instances disease spreads through contact. The concept of Quarantine is still in use to this day and is an example of how Pythagoras contributed to modern medicine even while his methods were based on “mystical aspects of the number system” Pythagoras and his followers did “attempt to use mathematics to quantify nature” and as a result, medical practice (Ede, Cormack,
The following three propositions are contained in Archimedes' book. The book also showed Archimedes had given the closest approximation of what we now call pi to date. i) The area of a circle is equal to that of a right-angled triangle where the sides, including the right angle, are equal to the radius and circumference of the circle.
Many years ago, in 355 CE to be exact, Hypatia was born. Hypatia is one of the world’s most well known mathematicians. Especially for her time, Hypatia was extremely bright and made many important discoveries and contributions to mathematics. Hypatia’s improvements shaped mathematics, and how we see them today. Hypatia's early life, accomplishments, and effects, and end of her life, all have importance and have shaped the world in mathematics.
The Greeks made other mathematical discoveries as well, however. Diophantus was the discoverer of fractions, and was an early scholar of algebra. Diphantus’ algebraic problems would become fruitful and inspiring mental exercises for future mathematicians for many centuries to come, like Plato’s Platonic Solids (Plato identified five three-dimensional shapes that were the only possible convex regular polyhedra) did for future mathematicians as well.
Greek mathematics began during the 6th century B.C.E. However, we do not know much about why people did mathematics during that time. There are no records of mathematicians’ thoughts about their work, their goals, or their methods (Hodgkin, 40). Regardless of the motivation for pursuing mathematical astronomy, we see some impressive mathematical books written by Hippocrates, Plato, Eudoxus, Euclid, Archimedes, Apollonius, Hipparchus, Heron and Ptolemy. I will argue that Ptolemy was the most integral part of the history of Greek astronomy.
One of the most well known contributors to math from Greece would be Archimedes. He
Ancient Greece's philosophers and mathematicians have made contributions to western civilizations. Socrates believed that a person must ask questions and seek to understand the world around them. Aristotle, another famous philosopher, is known for believing that if people study the origin of life, they will understand it more. Reasoning is what makes human beings unique. Hippocrates was a mathematician and a doctor. He created the Hippocratic oath. The oath states that Hippocrates will treat his patient to the best of his abilities that he will refuse to give deadly medicine. This oath is still used by doctors today. Another Greek mathematician was Euclid. His ideas were the starting point of geometry, which is still studied around the world today.
The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers.
Trigonometry is the branch of mathematics that is based on the study of triangles. This study helps defining the relations between the different angle measures of a triangle with the lengths of their sides. Trigonometry functions such as sine, cosine, and tangent, and their reciprocals are used to find the unknown parts of a triangle. Laws of sines and cosines are the most common applications of trigonometry that we have used in our pre-calculus class. Historically. Trigonometry was developed for astronomy and geography as it helped early explorers plot the stars and navigate the seas, but scientists have been using it for centuries for other purposes, too. Besides other fields of mathematics, it is used in physics,
The simplest forms of equations in algebra were actually discovered 2,200 years before Mohamed was born. Ahmes wrote the Rhind Papyrus that described the Egyptian mathematic system of division and multiplication. Pythagoras, Euclid, Archimedes, Erasasth, and other great mathematicians followed Ahmes (“Letters”). Although not very important to the development of algebra, Archimedes (212BC – 281BC), a Greek mathematician, worked on calculus equations and used geometric proofs to prove the theories of mathematics (“Archimedes”).
Trigonometry is one of the branches of mathematical and geometrical reasoning that studies the triangles, particularly right triangles The scientific applications of the concepts are trigonometry in the subject math we study the surface of little daily life application. The trigonometry will relate to daily life activities. Let’s explore areas this science finds use in our daily activities and how we use to resolve the problem.
There are many people that contributed to the discovery of irrational numbers. Some of these people include Hippasus of Metapontum, Leonard Euler, Archimedes, and Phidias. Hippasus found the √2. Leonard Euler found the number e. Archimedes found Π. Phidias found the golden ratio. Hippasus found the first irrational number of √2. In the 5th century, he was trying to find the length of the sides of a pentagon. He successfully found the irrational number when he found the hypotenuse of an isosceles right triangle. He is thought to have found this magnificent finding at sea. However, his work is often discounted or not recognized because he was supposedly thrown overboard by fellow shipmates. His work contradicted the Pythagorean mathematics that was already in place. The fundamentals of the Pythagorean mathematics was that number and geometry were not able to be separated (Irrational Number, 2014).
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.